Capital Asset Pricing Model

﻿

The 1990 Nobel Prize laureates for economics, Harry Markowitz
and William Sharpe, developed theories about the financial markets
that have had a profound effect on investors. Harry
Markowitz’s work pioneered what is now known as the modern
portfolio theory. Concerned with the composition of investments
that investors would select for their portfolios, Markowitz determined
that the major properties of an investment that should be of
concern to investors are risk and return. By choosing a range of
different investments for a portfolio, investors can determine and
control the total risk in that portfolio through variance analysis of
each investment. In other words, in plain English, investors can
assemble portfolios of risky stocks in which the risk of the whole
portfolio would be less than any of the individual stocks in the
portfolio. By determining the given amount of risk, investors select
the portfolio that offers the highest expected return.

A simple example illustrates this concept. Suppose that you
have a portfolio with equal amounts invested in two stocks: a
computer-related technology stock and a food stock. In good
economic times, when computer sales are growing, the price of
technology stocks is expected to increase by more than 50 percent,
and food stocks have an expected return of 6 percent (including
the dividends). During a recession, when computer sales are in the
doldrums, the price of the technology stock is expected to decline
by 20 percent. The food stock, however, because it is in a defensive
industry, is expected to increase by 40 percent. Thus, in a good
economy, the investors will earn an average return of 28 percent
[(50% + 6%)/2]. In a recession, the portfolio will earn an average
return of 10% [(40% - 20%)/2].

Although the technology stock is more risky than the food
stock, by diversifying into the two different industries, the average
returns are greater than if all the funds were invested in one stock.
In addition to reducing your risk by increasing the number of
stocks, you can reduce your risk by choosing stocks that react to
economic conditions differently.

William Sharpe and John Lintner further developed
Markowitz’s approach into the capital asset pricing model
(CAPM). The capital asset pricing model links the relationship
between risk and the expected return of a stock. The stock’s
expected rate of return is the risk-free rate plus a risk premium
based on the systematic risk of the stock. In this model, the risk of
a stock or portfolio is broken down into two parts: systematic and
unsystematic risk. The risk pertaining to the security itself (such as
business and financial risks) can be reduced and eliminated
through diversification. What remains is systematic risk, which
becomes important in the relationship between risk and return. In
other words, by combining several different stocks in a portfolio,
the unsystematic or diversifiable risk is reduced, and all that is left
is systematic risk. Systematic risk, also known as market risk, is the
relationship of a security’s price to changes in security prices in
the general market. Some stocks go up and down more than the
market, and other stocks fluctuate less than the market as a whole.
Systematic risk is measured by the Greek letter beta. The beta
coefficient, a measure of the systematic risk of a stock, links the
sensitivity of the stock’s rate of return to the rate of return of the
market and is determined as follows:

β = (standard deviation of the return of a stock/
standard deviation of the return of the market)
* correlation coefficient between return of the
stock and the market

The larger the standard deviation of the return of a stock relative
to the return of the market, the greater is the risk associated with that
stock. The correlation coefficient indicates the relative importance of
variability. The range of the correlation coefficient is from +1 to -1.
If the correlation coefficient is +1, the stock return and the market
return move together in a strong correlation. Thus, if the standard
deviation of the stock is 15 percent and the standard deviation of
the market is 10 percent with a correlation coefficient of 1, the beta
coefficient is 1.5

β = (standard deviation of the return of a stock/
standard deviation of the return of the market)
* correlation coefficient between return of the stock
and the market
= (0.15/0.10) * 1
= 1.5

A correlation coefficient of -1 with a standard deviation of a
stock equal to 8 percent and a standard deviation of 10 percent for
the market results in a beta of -0.8:

β = (0.08/0.10)* -1
= -0.8

A negative correlation coefficient results in the stock and the
market moving in opposite directions. If no relationship exists
between the return on the stock and the return on the market, then
the correlation coefficient is zero, which results in a beta coefficient
of 0, or no market risk.

For a stock with a beta coefficient of 1, if the market rises
by 20 percent, the stock price will increase by 20 percent. If the
market falls by 20 percent, the stock price also will see a
20 percent decline. The market is assumed to have a beta coefficient
of 1, which means that this stock is perfectly correlated with the
market.

Figure 12–3 illustrates the relationship between a stock with a
beta coefficient of 1.5 and the market with a beta of 1. The stock has
a return of 15 percent when the market increases by 10 percent. A
stock with a return that is less than the market is drawn below the
market line in the positive quadrant and it is drawn above the market
line in the negative quadrant. Thus a stock with a beta coefficient
greater than 1 should produce above-average returns in a bull
market and below-average returns in a bear market. Astock with a
beta coefficient of less than 1 is less responsive to market changes.
Investors who seek higher returns are willing to assume more risk.

Increased diversification into many different stocks in a portfolio
does not eliminate the systematic risk. In other words, these
stocks are not immune to a downturn in the market. However,
diversification into at least 20 different stocks can eliminate the
unsystematic risk, which is the risk that pertains to the company.
This includes financial, business, and purchasing-power risks,
which affect a company’s stock price.

Figure 12-3
Stock with a Beta Coefficient of 1.5

Table 12-3
Comparison of Beta Coefficients (October 18, 2006)
Calculating the beta coefficient is tedious. You can obtain beta
coefficients for individual stocks from several sources, such as
Value Line and Standard & Poor’s, which are subscription services,
and financial Web sites such as www.yahoo.com. You should not
be alarmed if you find different beta coefficients for the same stock
because beta coefficients can be derived using different market
measures, such as the S&P 500 Index versus the Value Line Index.
Similarly, discrepancies occur when the periods for the calculations
differ, using, for example, three years versus five years of price
data. Thus no correct beta coefficient exists. Table 12–3 compares
different beta coefficients.